Deformations of an elastic-plastic cylindrical shell with linear strain hardening

Plastic Bending of an Annular Plate

“…Boyce [7] used a piecewise linear approximation to the Mises yield curve, but was limited in the number of segments considered. Similarly, investigations of cylindrical shells by Hodge and others [8,9,10] have all been concerned with problems in which the stress point engaged in a regular progression.…”

“…(8) The hardening law in this case may be written [12] Mr CKr . (9) Finally, in place of the Inequalities 7, there must exist an equation stating that the stress point remains in the corner. For isotropic hardening the corner A is always on the Mr axis, hence M'P = o.…”

“…For isotropic hardening the corner A is always on the Mr axis, hence M'P = o. (10) At the inner boundary r = a, the displacement must vanish and the moment is prescribed; at infinity, the moment must tend to zero. Thus w(a) = 0, Mr(a) = M, Mr(oo) = o.…”

“…< r~ p, fJ. < r,(17)Since a particle was not strained in regime FA, the proper integral of Equation9 isMr -MoCKr . (18) Together with Equations 2 and 10 this determines the solution for a ~ r ~ fJ.. Boundary conditions are available at r = a and from continuity with Equations 17 at r = fJ..…”

The Theory of Rotationally Symmetric Plastic Shells

“…Hodge and his associates [25,26,27,28] have considered various simple problems in which elastic strains and strain-hardening were included. In every case investigated, a representative load-deformation curve had the qualitative form shown in Fig.…”